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Abstract:

Provided are methods and systems for determining the structure of a
composite or solid solution material for an electrode in lithium-ion
batteries. In one embodiment, a method is presented where a
building-block database of hypothetical structures containing only one
transition metal atom is constructed by use of quantum simulation. Then,
a composite model set of structures containing two or more transition
metal atoms is constructed by calculating a linear average of parent
components from the building-block database of hypothetical structures to
determine lattice constants and atomic coordinates of candidates. The
composite model set is screened with a local order matrix to subclassify
composite models into a subset, such that the composite models share the
same property in local transition metal ordering. Still yet, a
representative from each subset is selected and a quantum simulation on
the representative models is performed to determine the structure of the
material.

Claims:

1. A method of determining the structure of a composite or solid solution
material for a cathode in a lithium-ion battery, the method
comprising:constructing a building block database of hypothetical
structures containing only one transition metal atom in their crystal
unit cells by use of quantum simulation;constructing a composite model
set of structures containing two or more transition metal atoms by
calculating a linear average of parent components from the building block
database of hypothetical structures to determine the lattice constants
and atomic coordinates of candidate composition models, the structures
being nearby a total energy minimum;screening the composite model set by
employing a local order matrix to subclassify each composite model into a
subset such that the composite models in each subset share the same
property in local transition metal ordering, and selecting a
representative model from each subset; andperforming quantum simulation
on at least one of the representative models to determine the structure
of the composite or solid solution material.

2. The method of claim 1, wherein each of the structures from the
composite model set is within 2% of the corresponding quantum simulation
optimized structure determined from its representative model.

3. The method of claim 1, wherein each of the structures from the
composite model set is within 1% of the corresponding quantum simulation
optimized structure determined from its representative model.

5. The method of claim 1, wherein quantum simulation of the hypothetical
structures of the building block database is performed by the density
functional theory method or other similar quantum simulation methods.

6. The method of claim 1, wherein quantum simulation of the at least one
representative model is performed by the density functional theory method
or other similar quantum simulation methods.

7. The method of claim 1, wherein construction of the composite model set
of structures is performed with structures containing two or more
transition metal ions.

8. The method of claim 1, wherein quantum simulation is performed on two
or more of the representative models and the model with the lowest
formation energy is selected as the candidate structure for a composite
or solid solution material for an electrode in a lithium-ion battery.

9. The method of claim 8, wherein the formation energy is calculated at
30.degree. C. or less.

10. The method of claim 8, wherein the formation energy is calculated at
100.degree. C. or less.

11. The method of claim 8, wherein the formation energy is calculated at
200.degree. C. or less.

12. The method of claim 8, wherein the formation energy is calculated at
1200.degree. C. or less.

13. A method of determining the structure of a composite or solid solution
material for a cathode in a lithium-ion battery, the method
comprising:constructing a composite model set of structures containing
two or more transition metal atoms by calculating a linear average of
parent components from a building block database of hypothetical
structures containing only one transition metal atom in their crystal
unit cells to determine the lattice constants and atomic coordinates of
candidate composition models, the structures being nearby a total energy
minimum;screening the composite model set by employing a local order
matrix to subclassify each composite model into a subset such that the
composite models in each subset share the same property in local
transition metal ordering, and selecting a representative model from each
subset; andperforming quantum simulation on at least one of the
representative models to determine the structure of the composite or
solid solution material.

14. The method of claim 13, wherein each of the structures from the
composite model set is within 2% of the corresponding quantum simulation
optimized structure determined from its representative model.

15. The method of claim 13, wherein each of the structures from the
composite model set is within 1% of the corresponding quantum simulation
optimized structure determined from its representative model.

17. The method of claim 13, wherein quantum simulation of the at least one
representative model is performed by the density functional theory method
or other similar quantum simulation methods.

18. The method of claim 13, wherein construction of the composite model
set of structures is performed with structures containing two or more
transition metal ions.

19. The method of claim 13, wherein quantum simulation is performed on two
or more of the representative models and the model with the lowest
formation energy is selected as the candidate structure for a composite
or solid solution material for an electrode in a lithium-ion battery.

20. The method of claim 19, wherein the formation energy is calculated at
30.degree. C. or less.

21. The method of claim 19, wherein the formation energy is calculated at
100.degree. C. or less.

22. The method of claim 19, wherein the formation energy is calculated at
200.degree. C. or less.

23. The method of claim 19, wherein the formation energy is calculated at
1200.degree. C. or less.

24. A method of determining the structure of an alloyed anode material for
an electrode in a lithium-ion battery, the method comprising:constructing
a building block database of hypothetical structures containing only one
active backbone element in their crystal unit cells by use of quantum
simulation;constructing a composite model set of structures containing
two or more active backbone elements by calculating a linear average of
parent components from the building block database of hypothetical
structures to determine the lattice constants and atomic coordinates of
candidate composition models, the structures being nearby a total energy
minimum;screening the composite model set by employing a local order
matrix to subclassify each composite model into a subset such that the
composite models in each subset share the same property in local active
backbone element ordering, and selecting a representative model from each
subset; andperforming quantum simulation on at least one of the
representative models to determine the structure of the alloyed anode
material.

25. The method of claim 24, wherein each of the structures from the
composite model set is within 2% of the corresponding quantum simulation
optimized structure determined from its representative model.

26. The method of claim 24, wherein each of the structures from the
composite model set is within 1% of the corresponding quantum simulation
optimized structure determined from its representative model.

28. The method of claim 24, wherein quantum simulation of the hypothetical
structures of the building block database is performed by the density
functional theory method or other similar quantum simulation methods.

29. The method of claim 24, wherein quantum simulation of the at least one
representative model is performed by the density functional theory method
or other similar quantum simulation methods.

30. The method of claim 24, wherein construction of the composite model
set of structures is performed with structures containing two or more
active backbone elements.

31. The method of claim 24, wherein quantum simulation is performed on two
or more of the representative models and the model with the lowest
formation energy is selected as the candidate structure for an alloyed
anode material for an electrode in a lithium-ion battery.

32. The method of claim 31, wherein the formation energy is calculated at
30.degree. C. or less.

33. The method of claim 31, wherein the formation energy is calculated at
100.degree. C. or less.

34. The method of claim 31, wherein the formation energy is calculated at
200.degree. C. or less.

35. The method of claim 31, wherein the formation energy is calculated at
1200.degree. C. or less.

36. A method of determining the structure of an alloyed anode material for
an electrode in a lithium-ion battery, the method comprising:constructing
a composite model set of structures containing two or more active
backbone elements by calculating a linear average of parent components
from a building block database of hypothetical structures containing only
one active backbone element in their crystal unit cells to determine the
lattice constants and atomic coordinates of candidate composition models,
the structures being nearby a total energy minimum;screening the
composite model set by employing a local order matrix to subclassify each
composite model into a subset such that the composite models in each
subset share the same property in local active backbone element ordering,
and selecting a representative model from each subset; andperforming
quantum simulation on at least one of the representative models to
determine the structure of the alloyed anode material.

37. The method of claim 36, wherein each of the structures from the
composite model set is within 2% of the corresponding quantum simulation
optimized structure determined from its representative model.

38. The method of claim 36, wherein each of the structures from the
composite model set is within 1% of the corresponding quantum simulation
optimized structure determined from its representative model.

40. The method of claim 36, wherein quantum simulation of the at least one
representative model is performed by the density functional theory method
or other similar quantum simulation methods.

41. The method of claim 36, wherein construction of the composite model
set of structures is performed with structures containing two or more
active backbone elements.

42. The method of claim 36, wherein quantum simulation is performed on two
or more of the representative models and the model with the lowest
formation energy is selected as the candidate structure for an alloyed
anode material for an electrode in a lithium-ion battery.

43. The method of claim 42, wherein the formation energy is calculated at
30.degree. C. or less.

44. The method of claim 42, wherein the formation energy is calculated at
100.degree. C. or less.

45. The method of claim 42, wherein the formation energy is calculated at
200.degree. C. or less.

46. The method of claim 42, wherein the formation energy is calculated at
1200.degree. C. or less.

[0003]The invention relates to the use of quantum simulations to determine
the structure of composite/solid solution cathode and alloyed anode
materials.

[0004]2. Background of the Invention

[0005]Advanced batteries substantially impact the areas of energy storage,
energy efficiency, hybrid and plug-in electric vehicles, power tools,
laptops, cell phones and many other mobile electronic and entertainment
devices. Rechargeable lithium-ion batteries offer the highest energy
density of any battery technology and, therefore, are an attractive
long-term technology that now sustains a billion-dollar business. At the
materials level, over the last 30 years the major improvement in the
performance of lithium batteries has been achieved through the discovery
of new lithium cathode materials. LiTiS2 was the first
commercialized cathode material for lithium batteries in the 1970s.
LiCoO2 is currently the most active cathode material used in
lithium-ion batteries since its discovery in the early 1990s.

[0006]However, the safety and high cost of cobalt significantly limits its
application to the emerging high capacity and high power battery markets.
Additionally, the low charge and discharge rate capability is a
well-known problem of lithium-ion batteries (Kang et al., Science, 311:
977, 2006). Recent efforts in both industrial and academic attempts to
overcome these limitations have been focused on compositional
modification of LiCoO2, mainly by infusion with other transition
metal elements (Kang et al.; Shaju et al., Adv. Mater., 18: 2330, 2006;
Thackeray et al., U.S. Pat. No. 6,680,143), or new architectures for
advanced composite materials for cathodes.

[0007]There has been a similar interest in the development of an advanced
anode using alloyed materials since commercialization of the graphite
anode accompanying the LiCoO2 cathode in the 1990s (Winter et al.,
Chem. Rev., 104: 4245, 2004). Alloyed materials for an advanced anode and
composite materials for an advanced cathode are the mainstream approach
for next generation Li-ion battery technology. Both have the same nature
of disorder, in contrast to the well-defined crystalline structures of
LiCoO2 and graphite.

[0008]Searching for new materials by empirical experimental efforts is
time-consuming and expensive. Significant efforts are currently underway,
mainly in the academic community and Department of Energy laboratories to
use quantum simulations on high performance computers to accelerate the
search for new and better materials for the battery industry. The goals
of these efforts are: 1) to reduce the costs of the research and
development of a product; 2) to accelerate the time-cycle for new
material in a product from laboratory to market; and 3) to increase the
scope of systematic improvements in material designs. Quantum Simulations
(QS), based on the first-principles density functional theory (DFT) or
its equivalent, provide reliable computer simulations to predict on
atomic-scale the properties of currently known battery materials for
cathode, anode and electrolyte. The accuracy of the QS based predictions
of materials properties has been proven in a broad range of applications
in semiconductor to pharmaceutical industry.

[0009]It is in this context that embodiments of the invention arise.

SUMMARY

[0010]In one embodiment, a method of determining the structure of a
composite or solid solution material for a cathode in a lithium-ion
battery is presented. The method comprises:

[0011]constructing a building block database of hypothetical structures
containing only one transition metal atom in their crystal unit cells by
use of quantum simulation; constructing a composite model set of
structures containing two or more transition metal atoms by calculating a
linear average of parent components from the building block database of
hypothetical structures to determine the lattice constants and atomic
coordinates of candidate composition models, the structures being nearby
a total energy minimum;

[0012]screening the composite model set by employing a local order matrix
to subclassify each composite model into a subset such that the composite
models in each subset share the same property in local transition metal
ordering, and selecting a representative model from each subset; and

[0013]performing quantum simulation on at least one of the representative
models to determine the structure of the composite or solid solution
material.

[0014]Another embodiment presents a method of determining the structure of
a composite or solid solution material for a cathode in a lithium-ion
battery. The method comprises:

[0015]constructing a composite model set of structures containing two or
more transition metal atoms by calculating a linear average of parent
components from a building block database of hypothetical structures
containing only one transition metal atom in their crystal unit cells to
determine the lattice constants and atomic coordinates of candidate
composition models, the structures being nearby a total energy minimum;

[0016]screening the composite model set by employing a local order matrix
to subclassify each composite model into a subset such that the composite
models in each subset share the same property in local transition metal
ordering, and selecting a representative model from each subset; and

[0017]performing quantum simulation on at least one of the representative
models to determine the structure of the composite or solid solution
material.

[0018]In yet another embodiment, a method of determining the structure of
an alloyed anode material in a lithium-ion battery is presented. The
method comprises:

[0019]constructing a building block database of hypothetical structures
containing only one active backbone element in their crystal unit cells
by use of quantum simulation;

[0020]constructing a composite model set of structures containing two or
more active backbone elements by calculating a linear average of parent
components from the building block database of hypothetical structures to
determine the lattice constants and atomic coordinates of candidate
composition models, the structures being nearby a total energy minimum;

[0021]screening the composite model set by employing a local order matrix
to subclassify each composite model into a subset such that the composite
models in each subset share the same property in local active backbone
element ordering, and selecting a representative model from each subset;
and

[0022]performing quantum simulation on at least one of the representative
models to determine the structure of the alloyed anode material.

[0023]In still another embodiment, a method of determining the structure
of an alloyed anode material for an electrode in a lithium-ion battery is
presented. The method comprises:

[0024]constructing a composite model set of structures containing two or
more active backbone elements by calculating a linear average of parent
components from a building block database of hypothetical structures
containing only one active backbone element in their crystal unit cells
to determine the lattice constants and atomic coordinates of candidate
composition models, the structures being nearby a total energy minimum;

[0025]screening the composite model set by employing a local order matrix
to subclassify each composite model into a subset such that the composite
models in each subset share the same property in local active backbone
element ordering, and selecting a representative model from each subset;
and

[0026]performing quantum simulation on at least one of the representative
models to determine the structure of the alloyed anode material.

[0027]Other methods, features and advantages of the present invention will
be or become apparent to one with skill in the art upon examination of
the following detailed descriptions. It is intended that all such
additional methods, features and advantages be included within this
description, be within the scope of the present invention, and be
protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0028]The invention may best be understood by reference to the following
description taken in conjunction with the accompanying drawings in which:

[0029]FIG. 1 shows a schematic diagram of the algorithm for designing and
optimizing solid-solution/composite materials for lithium-ion batteries
using quantum simulations.

[0032]FIG. 4 shows the configuration distribution statistics for
optimizing the structure of Li(CoNiMn1/3O2.

[0033]FIG. 5 depicts a computer environment for implementing embodiments
of the invention.

[0034]FIG. 6 illustrates a flow chart for a method of determining the
structure of a composite or solid solution material for a cathode in a
lithium-ion battery.

DETAILED DESCRIPTION

[0035]Before the present compositions and methods are described, it is to
be understood that the invention is not limited to the particular
methodologies, protocols, assays, and reagents described, as these may
vary. It is also to be understood that the terminology used herein is
intended to describe particular embodiments of the present invention, and
is in no way intended to limit the scope of the present invention as set
forth in the appended claims.

[0036]It must be noted that as used herein and in the appended claims, the
singular forms "a," "an," and "the" include plural references unless the
context clearly dictates otherwise.

[0037]Unless defined otherwise, all technical and scientific terms used
herein have the same meanings as commonly understood by one of ordinary
skill in the art to which this invention belongs. All publications cited
herein are incorporated herein by reference in their entirety for the
purpose of describing and disclosing the methodologies, reagents, and
tools reported in the publications that might be used in connection with
the invention. Nothing herein is to be construed as an admission that the
invention is not entitled to antedate such disclosure by virtue of prior
invention.

[0038]As used herein, the term "total energy minimum" is an equivalent
term for "structural stability" and indicates synthesis feasibility as
commonly understood technical and scientific terminology.

[0039]As used herein, the term "local order matrix" is a measurement of
the like-elements distribution near transition metal elements or active
backbone elements in distance. This includes the first nearest neighbors,
the second nearest neighbors, and even higher order nearest neighbors if
needed.

[0040]As used herein, the term "linear average" is the commonly used math
expression xave=(Σxi, where i ranges from 1 to n)/n,
where xi is the i-th component of the n-parent structures.

[0041]Two unique difficulties limit the application of Quantum Simulations
(QS) to search and optimization for lithium-ion battery materials on a
regular basis: 1) the complexity of compositional modification and
ensuing solid solution or composite structure determination; 2) the large
number of degrees of freedom and complex interactions in transition metal
elemental species in solid solution and composite materials.

[0042]The possible schemes to modify a composition are numerous. For
example, to replace Co in LiCoO2 by m-elements of the first row
transition metals could have 10m possibilities (total combination of
m-members from 10 different elements). The experimental techniques can
only control the relative mole ratio of compositions; the individual
atoms in solid solution materials cannot be determined by regular crystal
structure characterization methods. Therefore, the detailed atomic
arrangement is at large for a given ratio solid solution. This hinders
the assessing of material property by QS.

[0043]Unlike semiconductor elements, the electronic structures of
transition metals are much more complex and demand higher accuracy QS.
Due to the cubic scaling of the time to the number of atoms in the
material models, the QS for big models on a first-principles basis remain
a formidable task even for materials containing very simple elements. For
example, in recent highly accurate modeling of a carbon-based system with
180 atoms, the computational time to determine the binding energy was
1500 CPU hours (or 63 CPU days) using supercomputers (Williamson et al.,
Physical Review Letters, 87: 246496, 2001). Modeling solid solution or
composite materials including transition metal elements for battery
applications inevitably requires large supercells that could contain from
several tens to hundreds of atoms in thousands of combinatorial mixtures.
For example, in recent studies, a supercell with 511 atoms has been used
to model a dilute concentration of vacancies in LixCoO2
(x<1%) (Marianetti et al., Nature Materials, 3: 627, 2004).

[0044]The principle of material modeling by QS is based on the trial and
error strategy to search a candidate structure located on a total energy
minimum in a multi-dimensional space spanned by 6 lattice constants and
3N coordinate variables of N-atoms per unit cell. However, to deduce the
coordinates of a possible structure starting with a random arrangement of
atoms is a computationally demanding task, and currently impossible for
complex materials. The efficiency of a high-throughput search of new
materials using QS thus is dependent on the starting point on the
multi-dimensional landscape or the hypothetical framework structures. The
initial trial structures are often drawn from the researcher's empirical
experience on the available data, and unfortunately there is no universal
discipline to guarantee such a guess to be good for yet unsynthesized
materials.

[0045]Thus, the main bottleneck in the use of QS for high-throughput
search and optimization of advanced battery materials is the lack of an
efficient and fast search algorithm that can avoid large utilization of
computing resources and, more importantly, the time in the search and
optimization of the complex composite and solid-solution materials in the
multi-dimensional landscape. A reliable and efficient search strategy or
algorithm will narrow down the likely range of candidate structures in
the vast dimensional search space, and a fast high-throughput search
engine using QS would be feasible for design and optimization of new
lithium-ion battery materials for high power, capacity, and better
stability applications in a timely manner.

[0046]Therefore, the present inventors have developed a search algorithm
for fast and high-throughput design and optimization of
solid-solution/composite materials for lithium-ion batteries using QS.

[0047]Our fast and high-throughput search algorithm is based on two facts:
1) advances in parallel computing platforms have made feasible highly
accurate QS on small crystals which are very efficient on moderate
computing resources on a regular basis, and 2) the crystal structures of
the solid-solution and composite materials for lithium-ion battery
applications are generally a derivative of the constitutive parent
crystals. The algorithm is outlined in FIG. 1. Each module is further
described below.

[0048]The first module 102 is construction of a building blocks database
by highly accurate QS. Building blocks are "Lego Units", which are a
hypothetical structure containing only one transition metal atom in their
crystal unit cells. This simplicity makes conventional, accurate QS
search of new architectures possible in a timely manner. For example,
replacing Co in layered (or spinel) LiCoO2 or Fe in LiFePO4 by
other transition metal elements forms a new constitutive crystal to be
used later as a component of solid solution models. The "Lego Units" may
or may not be physically feasible or synthesized in the laboratory, and
yet could serve as the computationally derived building blocks to
determine the search criteria and domain of more complex solid solution
or composite materials that are feasible and can be synthesized for
lithium-ion battery applications.

[0049]The second module 104 is to construct a relatively complete big
composite model set from "Lego Units" building blocks given by the first
module. Our construction algorithm, as indicated in FIG. 1, determines
the geometry of composite models, i.e., the lattice constants and atomic
coordinates. The structure determined by this simple algorithm is within
1-2% of the corresponding QS optimized structure and experimental data.
In other words, this algorithm creates initial structures nearby a total
energy minimum without any ad-hoc input from experimental measurements.
This significantly narrows the range of search landscape needed for the
complex solid solution and composite materials.

[0050]The third module 106 is a quick structural screening. Because the
model set from the second module often contains thousands of models (an
example is given in the next section), a structural screening criterion
is implemented to select representative models for a target composite
ratio. Because of the nature of disorder, the structure of solid
solutions is characterized statistically by a local order matrix, which
measures the local chemical environment of a composite material. By
tracking those matrix elements, the full model set can be classified into
several smaller subsets groups. Representative models from each group
form a compact set of target composite models.

[0051]The fourth module 108 is a final QS screening on representative
models from the third module. Because the number of candidates has been
significantly reduced in the third module and their initial structures
are by construction nearby a total energy minimum as determined in the
second module, the algorithm guarantees a fast and high-throughput search
through a large model set.

[0052]The knowledge and information gained from the first, second, third
and fourth modules is then iteratively used to (a) refine the predictive
capability of the search algorithm and method, and (b) successively build
larger and more complex secondary, tertiary and higher order structures
depending upon the crystal structures satisfying the Lego-like building
and compatibility criteria from smaller units.

[0053]Until now, materials discovery or design has largely been accidental
and primarily driven by empirical experimental methods. The process of
bringing an optimal material to market is quite slow in the battery
industry. It took twenty years to move from LiTiS2 to LiCoO2
and another 15 years so far for design of a new generation of cathode
material to occur. Designing advanced materials by computer will
accelerate this process only if fast and high-throughput screening and
predictions of new materials are possible in a cost and time-effective
manner. One objective is to rapidly screen through hundreds to thousands
of solid solutions or composite battery materials to short-list the few
candidate materials which could be recommended for detailed
investigations via either highly accurate QS or experimental synthesis
and characterization methods. In one embodiment, a QS database of small
"Lego like" structures is used with a screening algorithm for
implementation in a fast and high-throughput search engine to
significantly reduce design and optimization costs on one hand and
shorten search time on the other.

[0054]The present method does not depend on any specific QS technique for
building the searchable database of constitutive "Lego like" parent unit
cell structures. Any existing QS can be embedded in building the core of
the searchable database and the search engine. Accuracy of the search
engine will depend on the accuracy of the QS technique used, and any
advances in the QS techniques could be iteratively incorporated to
further speed up the efficiency of the developed first generation search
engine.

[0055]The present method does not depend on a specific electrode prototype
and, therefore, minimizes the need of background experience.

[0056]The present search engine is easy to implement on moderate parallel
computing platforms or clusters with current QS technologies, and does
not essentially depend on the availability of high-power supercomputers
for the largest size scale simulations. However, future advances in
computer hardware and software technology as well as QS efficiency and
accuracy can be iteratively incorporated to further improve the
predictive accuracy and range of the developed search engine.

[0057]Once a complex composite or solid solution candidate structure is
determined or predicted by the search engine, its physical and chemical
properties can be reliably calculated by highly accurate QS. Specific
application properties can be easily sought according to simple battery
principles. For example, the calculation of formation energy offers a
fast screening of material stability and feasibility of synthesis; the
calculation of average open circuit voltage predicts a possible working
voltage range for a candidate material.

[0058]The above discussion has focused on methods for determining the
structure of a composite or solid solution material for an electrode in a
lithium-ion battery. More particularly, such materials are typically used
in a cathode. Transition metal atoms for the composite or solid solution
materials include Sc, Ti, Zr, V, Nb, Cr, Mo, W, Mn, Fe, Co, Ni, Cu, Pd,
Pt, Tc, Ru, Rh, Cd, Ag, Au, Y and Zn.

[0059]The methods described herein may also be used, for example, for
determining the structure of an alloyed anode material in a lithium-ion
battery. In such methods for alloyed anode materials, one merely
substitutes an active backbone element in the structure of the alloyed
anode material like the transition metal atoms in the composite or solid
solution material for a cathode. Active backbone elements for the alloyed
anode material include B, Al, Ga, C, Si, Ge, Sn, N, P, Sb, Bi, O, S, Se,
Te, Zn, Cu, Ag and Au.

[0060]The use of such a computational approach in material designs without
the need of experimental input should greatly accelerate the discovery of
new classes of battery materials. Computational design of hypothetical
new materials is possible, including the study of stability and
prediction of properties, and is timely for the lithium-ion battery
industry.

[0061]These and other embodiments of the present invention will readily
occur to those of ordinary skill in the art in view of the disclosure
herein, and are specifically contemplated.

[0062]The invention is further understood by reference to the following
examples, which are intended to be purely exemplary of the invention. The
present invention is not limited in scope by the exemplified embodiments,
which are intended as illustrations of single aspects of the invention
only. Any methods that are functionally equivalent are within the scope
of the invention. Various modifications of the invention in addition to
those described herein will become apparent to those skilled in the art
from the foregoing description. Such modifications fall within the scope
of the appended claims.

EXAMPLE 1

[0063]Described here is a procedure to search a candidate structure using
an example having a specific composition, i.e.,
Li(CoNiMn)1/3O2. The results prove the reliability of the
algorithm and analyze the saving in computation costs. This validates the
strategy as a fast and high-throughput search of candidate structures for
lithium-ion battery materials.

[0064]The target composition Li(CoNiMn)1/3O2 has three
transition metal elements: Co, Ni, and Mn. Thus, the first operation
determines structural parameters of three constitutive components:
LiCoO2, LiNiO2, and LiMnO2 by QS. The layered LiCoO2
structure is defined by two lattice parameters, (i.e. a and c) and
contains four atoms per unit cell. Since the crystalline parameters of
LiCoO2 and LiNiO2 have been measured, experimental data are
used as starting points in QS structural optimization. Table 1 compares
QS optimized structures of LiCoO2 and LiNiO2 with their
experimental data. The structural parameters of both models agree with
measurements within about 1%. The LiMnO2 has not been a reported
synthesized material in layered phase; its lattice parameters and atomic
positions are unknown. To determine a computational model of LiMnO2,
a trial-and-error strategy was used to locate a stable point on the
energy surface. In this trial-and-error search, the structural parameters
of optimized LiCoO2 were used as the initial structure and Co was
replaced by Mn. The corresponding energy surface is shown in FIG. 2. The
computing costs of this scanning are listed in Table 2.

[0065]The second operation constructs a relatively complete set of large
scale composite models that have an equal mole ratio among Co, Ni and Mn
from the database determined in the foregoing paragraph. An R30 structure
(shown in FIG. 3) was used as a template, which is a supercell of the
layered LiCoO2. The R30 structure has 36 atoms per unit cell and
provides a template to simulate all the essential configurations having
equal mole ratios of Co, Ni, and Mn atoms. Each configuration has a
different distribution of Co, Ni and Mn atoms in the supercell and thus
has different structural parameters that are determined from the
aforementioned database by the construction algorithm indicated in FIG.
1. This construction algorithm results in 1680 different composite
models. Two examples are illustrated in FIG. 3. The structures determined
by the construction algorithm are near stable points on the
multi-dimensional energy landscape. As presented in Table 3, the
structures from the algorithm are within about 1-2% of QS optimized
structures. This accuracy is also close to the QS error with respect to
experimental structures as indicated in Table 1. This proves that the
algorithm-derived structures can be used alone for further analysis or as
a good starting point for QS optimizations.

[0066]The third operation in structure screening is to find representative
models from the model set given by the previous paragraph for the target
composite material. Computing a single model of 36 atoms per cell is a
moderate cost for QS. However, if computing one structure requires one
day, a full scan of the 1680 models by QS would take 4.6 years. We employ
a local order matrix to subclassify or screen the 1680 models. As shown
in FIG. 3, different models have very different matrices, which measure
the detailed transition metal atomic ordering. From the order matrix, the
1680 models are screened or classified into only five different groups as
showed in FIG. 4. Models in the same group share the same property in the
local transition metal ordering. Thus, only a limited number of
representative models is needed for the target composite,
Li(CoNiMn)1/3O2, without loss of generality.

[0067]The last operation performs QS on the representative models selected
from the previous paragraph. The number of candidates has been
significantly reduced and these hypothetical structures are located in a
valley on the multidimensional energy landscape. These bring QS
significant efficiency by scanning only those points near the bottom of
the valley of the energy surface. Formation energy given by QS shown in
Table 3 offers a further screening criterion. Because the model B has
positive formation energy with respect to three individual components, it
is not an energetically favorite phase. Therefore, among the choices A
and B only model A could be further considered as a likely candidate for
the battery materials. Using this approach, kinetically stable phases can
be identified on the valleys of the potential energy at low temperature,
while a more complex minimization of the free energy is required to
identify high-temperature phases from the selected candidates.
Furthermore, a similar "Lego like" building block approach can be used to
a) introduce transition metals other than Co, Ni, and Mn in the mix and
b) include all other phases of Li(M)O2 type materials for
optimization of required energy and power densities.

EXAMPLE 2

[0068]Described here is a procedure to search a candidate structure using
an example having a specific composition, i.e.,
Li(Co2/9Ni4/9Mn1/3)O2. The results prove the
reliability of the algorithm. This validates the strategy as a fast and
high-throughput search of candidate structures for lithium-ion battery
materials.

[0069]This target material has a different mole ratio among the
constitutional transitional metal elements from the previous example. The
first operation is the same as in Example 1. The second operation
constructs a relatively complete set of large-scale composite models that
have the mole ratio (2/9, 4/9, 1/3) among Co, Ni and Mn using the same
R30 template. The construction algorithm indicated in FIG. 1 results in
1260 different composite models.

[0070]The next operation uses the local order matrix to classify the 1260
models into a smaller subset of eight representative models. Further QS
is only needed for the eight representative models.

EXAMPLE 3

[0071]Described here is a procedure to search a candidate using an example
having a specific composition, i.e.,
Li(Fe1/9Ni5/9Mn1/3)O2. The results prove the
reliability of the algorithm.

[0072]This target material has a different mole ratio and constitutional
transition metal elements from the previous two examples. Furthermore,
LiFeO2 is not an experimentally well-defined structure. Thus, the
first operation of Example 1 is performed in order to determine the data
needed in the following operations. The second operation constructs a
relatively complete set of large-scale composite models that have the
mole ratio (1/9, 5/9, 1/3) among Fe, Ni and Mn using the same R30
template. The construction algorithm indicated in FIG. 1 results in 504
different composition models. The next operation uses the local order
matrix to classify the 504 models in a smaller subset of five
representative models. Further QS is only needed for the five
representative models.

[0073]Examples 2 and 3 illustrate the advantages of implementing the
present search engine for varying the ratio and transition metal
composition of Li-ion battery electrodes. This validates the strategy as
a fast and high-throughput search of candidate structures for lithium-ion
battery materials.

[0074]Finally, we give an estimate on the saving of time due to use of the
algorithm-derived structures as a starting point in QS optimization.
Table 2 gives a comparison of QS optimization between LiMnO2 and
composite Li(CoNiMn)1/3O2 Model A. Even though these two models
are quite different, the path passed from starting points to stable
points on the energy surface gives a clear perspective on the saving of
time for large structures. As shown in Table 2, compared to the 197 total
points investigated in the search of a stable LiMnO2 phase, the
trial points of the composite Li(CoNiMn)1/3O2 Model A are
reduced by a factor of 10 if searched using the algorithm-derived
structures. A broader range of energy points is avoided for the large
composite structure. The rather extensive and expensive QS in our method
are used to fine tune the algorithm-derived structures. Furthermore,
because of the substantial increase of computing costs required at each
structural point of the large model, the total computing costs are
significantly reduced. Thus, the algorithm uses only those structures
with high probability to be successfully synthesized in an economic and
timely manner.

[0075]FIG. 5 depicts a computer environment for implementing embodiments
of the invention. It should be appreciated that the methods described
herein may be performed with a digital processing system, such as a
conventional, general-purpose computer system. Special purpose computers,
which are designed or programmed to perform only one function may be used
in the alternative. The computer system includes a central processing
unit (CPU) 504, which is coupled through bus 510 to random access memory
(RAM) 506, read-only memory (ROM) 512, and mass storage device 514.
Quantum simulation program 508 resides in random access memory (RAM) 506,
but can also reside in mass storage 514.

[0076]Mass storage device 514 represents a persistent data storage device
such as a floppy disc drive or a fixed disc drive, which may be local or
remote. Network interface 530 provides connections via network 532,
allowing communications with other devices, such as search server 114,
community bookmark server 112 as seen in FIG. 1. It should be appreciated
that CPU 504 may be embodied in a general-purpose processor, a special
purpose processor, or a specially programmed logic device. Input/Output
(I/O) interface provides communication with different peripherals and is
connected with CPU 504, RAM 506, ROM 512, and mass storage device 514,
through bus 510. Sample peripherals include display 518, keyboard 522,
cursor control 524, removable media device 534, etc.

[0077]Display 518 is configured to display the user interfaces described
herein, such as browser 102 from FIG. 1. Keyboard 522, cursor control
524, removable media device 534, and other peripherals are coupled to I/O
interface 520 in order to communicate information in command selections
to CPU 504. It should be appreciated that data to and from external
devices may be communicated through I/O interface 520. The invention can
also be practiced in distributed computing environments where tasks are
performed by remote processing devices that are linked through a
wire-based or wireless network.

[0078]FIG. 6 illustrates a flow chart for a method of determining the
structure of a composite or solid solution material for a cathode in a
lithium-ion battery. In operation 602, the method constructs a building
block database of hypothetical structures containing only one transition
metal atom in their crystal unit cells by use of quantum simulation. In
operation 604, the method constructs a composite model set of structures
containing two or more transition metal atoms by calculating a linear
average of parent components from the building block database of
hypothetical structures to determine the lattice constants and atomic
coordinates of candidate composition models. Te structures are nearby a
total energy minimum.

[0079]Further, in operation 606 the method screens the composite model set
by employing a local order matrix to subclassify each composite model
into a subset such that the composite models in each subset share the
same property in local transition metal ordering, and selecting a
representative model from each subset. In operation 608, the method
performs a quantum simulation on at least one of the representative
models to determine the structure of the composite or solid solution
material.

[0080]Embodiments of the present invention may be practiced with various
computer system configurations including hand-held devices,
microprocessor systems, microprocessor-based or programmable consumer
electronics, minicomputers, mainframe computers and the like. The
invention can also be practiced in distributed computing environments
where tasks are performed by remote processing devices that are linked
through a wire-based or wireless network.

[0081]With the above embodiments in mind, it should be understood that the
invention can employ various computer-implemented operations involving
data stored in computer systems. These operations are those requiring
physical manipulation of physical quantities. Any of the operations
described herein that form part of the invention are useful machine
operations. The invention also relates to a device or an apparatus for
performing these operations. The apparatus can be specially constructed
for the required purpose, or the apparatus can be a general-purpose
computer selectively activated or configured by a computer program stored
in the computer. In particular, various general-purpose machines can be
used with computer programs written in accordance with the teachings
herein, or it may be more convenient to construct a more specialized
apparatus to perform the required operations.

[0082]The invention can also be embodied as computer readable code on a
computer readable medium. The computer readable medium is any data
storage device that can store data, which can be thereafter be read by a
computer system. Examples of the computer readable medium include hard
drives, network attached storage (NAS), read-only memory, random-access
memory, CD-ROMs, CD-Rs, CD-RWs, magnetic tapes and other optical and
non-optical data storage devices. The computer readable medium can
include computer readable tangible medium distributed over a
network-coupled computer system so that the computer readable code is
stored and executed in a distributed fashion.

[0083]Although the method operations were described in a specific order,
it should be understood that other housekeeping operations may be
performed in between operations, or operations may be adjusted so that
they occur at slightly different times, or may be distributed in a system
which allows the occurrence of the processing operations at various
intervals associated with the processing, as long as the processing of
the overlay operations are performed in the desired way.

[0084]It will be appreciated that, although specific embodiments of the
invention have been described herein for purposes of illustration,
various modifications may be made without departing from the spirit and
scope of the invention. All such modifications and variations are
intended to be included herein within the scope of this disclosure and
the present invention and protected by the following claims.